In this paper, we provide exponential rates of convergence to the Nash equilibrium for continuous-time dual-space game dynamics such as mirror descent (MD) and actor-critic (AC). We perform our analysis in $N$-player continuous concave games that are either potential games or monotone games but possibly potential-free. In the first part of this paper, we provide a novel relative characterization of monotone games and show that MD and its discounted version converge with $\mathcal{O}(e^{-\beta t})$ in relatively strongly and relatively hypo-monotone games, respectively. In the second part of this paper, we specialize our results to games that admit a relatively strongly concave potential and show that MD and AC converge with $\mathcal{O}(e^{-\beta t})$. Moreover, these rates extend their known convergence conditions. Simulations are performed which empirically back up our results.

翻译：在本文的第一部分,我们提供了与Nash平衡的指数性趋同率,用于连续时间的双空间游戏动态,如镜底(MD)和演员-critic(AC)等。我们用美元玩家连续的组合游戏进行分析,这些游戏可能是潜在的游戏或单调游戏,但可能是没有的。在本文的第一部分,我们提供了单调游戏的新颖相对特征,并显示MD及其折扣版与$mathcal{O}(e\\\\\\beta t})(e\\\\\\beta t})($ mathcal{O}(e\\\\\beta t})(e\mathcal{O})(e\\\\beta t})(e\\\beta t})(e\\\\\\beta t}(e\\\\\\ a)相配合。在相对强和相对低调的游戏中。在本文的游戏中,我们把我们的结果专门用于承认相对强烈的组合潜力的游戏,显示MDDD和AC会合。